SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5598-5626, January 2020.
We consider a Caratheodory differential equation with a state-dependent convex constraint that changes BV-continuously in time (a perturbed BV-continuous state-dependent sweeping process). By setting up an appropriate catching-up algorithm we prove solvability of the initial value problem. Then, for sweeping processes with $T$-periodic right-hand sides, we prove the existence of at least one $T$-periodic solution. Finally, we investigate a $T$-periodic sweeping process which is close to an autonomous sweeping process with a constant constraint and prove the existence of a $T$-periodic solution specifically located near the boundary switched equilibrium of the autonomous sweeping process.

中文翻译：

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周期性BV连续状态依存的清扫过程的延续原理

SIAM数学分析期刊，第52卷，第6期，第5598-5626页，2020年1月。
我们考虑具有状态依赖凸约束的Caratheodory微分方程，该约束随时间连续变化BV（扰动的BV连续状态依赖扫描处理）。通过设置适当的追赶算法，我们证明了初值问题的可解性。然后，对于带有$ T $周期右手边的清扫过程，我们证明了至少存在一个$ T $周期解。最后，我们研究了$ T $-周期扫描过程，该过程接近于具有恒定约束的自治扫描过程，并证明了$ T $-周期解的存在，该解特别位于自治扫描过程的边界切换平衡附近。